Meridian Surfaces on Rotational Hypersurfaces with Lightlike Axis in ${\mathbb{E}}_2^4$

Abstract

We construct a special class of Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with lightlike axis and call them meridian surfaces. We give the complete classification of the meridian surfaces with constant Gauss curvature and prove that there are no meridian surfaces with parallel mean curvature vector field other than CMC surfaces lying in a hyperplane. We also classify the meridian surfaces with parallel normalized mean curvature vector field. We show that in the family of the meridian surfaces there exist Lorentz surfaces which have parallel normalized mean curvature vector field but not parallel mean curvature vector.

12 pages. arXiv admin note: substantial text overlap with arXiv:1606.00047

References in corpus (5)

• Submanifolds with parallel mean curvature vector in Riemannian and indefinite space forms
• Marginally trapped meridian surfaces of parabolic type in the four-dimensional Minkowski space
• Meridian Surfaces in E^4 with Pointwise 1-type Gauss Map
• Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-space with Neutral Metric
• Meridian Surfaces with Parallel Normalized Mean Curvature Vector Field in Pseudo-Euclidean 4-space with Neutral Metric